Theorem of the Day (December 26, 2025) : The Marriage Theorem and The Frobenius–Konig Theorem.
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/Marriage/TotDMarriage.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#62
Now this animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ https://decompwlj.com
A little more work on axis sizing and controls.
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Decomposition into weight × level + jump with 3D graphs (WebGL three.js), 2D graphs and first 500 terms. This decomposition is an extension of the fundamental theorem of arithmetic and a new way to see the numbers. 1000 sequences decomposed (natural numbers, prime numbers, triangular numbers, composites...). Rémi Eismann
4: The palindromes in base 10 (A002113) ➡️ https://decompwlj.com/3DgraphGen/Palindromes.html
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3: The triangular numbers (A000217) ➡️ https://decompwlj.com/3DgraphGen/Triangular_numbers.html
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
2: The prime numbers (A000040) ➡️ https://decompwlj.com/3DgraphGen/Prime_numbers.html
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
🧵⬇️
1: The natural numbers (A000027) ➡️ https://decompwlj.com/3DgraphGen/Natural_numbers.html
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
A066031: Composite numbers n the sum of whose prime factors divides n, but which are not themselves powers of primes
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A066031.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A066031.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A066031.html
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
150 sequences decomposed into weight × level + jump in one GIF (log(weight),log(level)):
1000 sequences decomposed on https://decompwlj.com
#decompwlj #math #mathematics #maths #sequence #OEIS #graph #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
A065496: Numbers n such that sigma(n) is a nontrivial power, i.e., sigma(n) = a^b where a and b are greater than 1.
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A065496.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A065496.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A065496.html
#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research
Theorem of the Day (December 25, 2025) : The Existence Theorem for Orthogonal Diagonal Latin Squares
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/CombinatorialTheory/DDOLS/TotDDDOLS.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#131
Paysages Mathématiques
Rémi Eismann